Abstract
In a recent investigation of the displacement suffered by two spatial solitons approaching each other some general coupled equations were used1-3. They describe the complete nonlinear interaction between two spatial solitons, with the same frequency and polarisation, located in a pair of, identical, coupled slab waveguides (1 and 2) and have the form, where propagation is along the z-axis, beam confinement by the nonlinearity is along the x-axis, modal confinement is along the y-axis, k = 3-i, i = 1,2, ψi and ψk are normalised slowly varying amplitudes of the electric fields in the guides, ν represents the inter-guide coupling and μ1, μ2 are nonlinear coefficients. The first point to make is that these coupled equations go far beyond the classical work of Jensen4 and will only return to it5 provided that the last four terms are neglected. Indeed, some of the usually neglected terms are larger than the terms that are, normally, retained and, therefore, have a crucial influence on the stability and the threshold powers of the spatial solitons. The second point is that a full variational solution of the coupled equations can be made to yield a mathematical, analytical, nonlinear stability analysis, generating switching formulae with tractable forms for the stability edges, or thresholds. Even within a Jensen model, the results to be presented here are entirely new and it should be stressed that all the parameters ν, μ1 and μ2 are required for inter-guide interactions. A Jensen formalism, on the other hand, involving ν and only one other parameter μ, is adequate for intra-guide polarisation interactions. The objectives here are (a) to present a mathematical and numerical solution of the general coupled equations that will account for energy exchange between spatial solitons (b) to generate a theory of stability for solitons hovering, one above the other, in the respective guides (c) to investigate the possibilities for modulation instability.
© 1993 Optical Society of America
PDF ArticleMore Like This
A.D. Boardman and K. Xie
IWF2 Integrated Photonics Research (IPR) 1993
J. S. Aitchison
MA.1 Nonlinear Guided-Wave Phenomena (NP) 1993
AD Boardman and K Xie
PD.6 Nonlinear Guided-Wave Phenomena (NP) 1993